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| PAGE: 776 | SET: Exercises | PROBLEM: 15 |
The function is 
.
Apply derivative on each side with respect to 
.
.
Power series formula: 
.
Apply integral on each side.
.
Substitute 
in 
.
.
Substitute 
in .
.
The power series representation 
is 
.
Find the radius of converence.
Consider 
and 
.
Ratio test :
Let 
be a series with non zero terms.
1. converges absolutely if 
.
2. diverges if 
or 
.
3. The ratio test is inconclusive if 
.
Find 
.
.
The series is converges when 
.
.
Therefore, the radius of the convergence is 
.
The power series representation is .
The radius of the convergence is .
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